On the Existence of Spacetime Structurey Erik Curielz ABSTRACT I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no clear criterion to distinguish the positions. I propose two such precise criteria and construct separate arguments based on each to yield contrary conclusions, one supportive of something like relationalism and the other of something like substantivalism. The lesson is that one must fix an investigative context in order to make such criteria precise, but different investigative contexts yield inconsistent results. I examine questions of existence about spacetime structures other than the spacetime manifold itself to argue that it is more fruitful to focus on pragmatic issues of physicality, a notion that lends itself to several different explications, all of philosophical interest, none privileged a priori over any of the others. I conclude by suggesting an extension of the lessons of my arguments to the broader debate between realists and instrumentalists. yThis paper is forthcoming in British Journal for Philosophy of Science, 2015. zI owe a great debt to Howard Stein's papers \Yes, but. : Some Skeptical Remarks on Realism and Anti-Realism" and \Some Reflections on the Structure of Our Knowledge in Physics", both of which inspired the paper's spirit. I am not sure whether Prof. Stein would endorse the paper's methods. I have hopes he would. It is a pleasure to thank the Philosophy Department at Carnegie Mellon for tough questioning after a colloquium in which I presented an earlier version of this paper, and in particular Richard Scheines, Teddy Seidenfeld and Peter Spirtes for pushing me on the arguments of x3; I thank as well the philosophy of physics reading group at Irvine, and especially Jim Weatherall, arXiv:1503.03413v1 [physics.hist-ph] 11 Mar 2015 for penetrating questions about x3. The paper is much stronger for my attempts to address their skepticism. I also thank the Fellows at the Center for Philosophy of Science (2008{2009) at Pitt and several graduate students in the History and Philosophy of Science Department and the Philosophy Department at Pitt for insightful questions after an informal presentation of the paper. I am grateful to Jeremy Butterfield for graciously harsh comments on an early draft. John Norton, much as I suspect he would like to, cannot escape my gratitude for conversations in which he effortlessly showed me how to present simply what I could see only as complex. And I thank Howard Stein and David Malament, as always, for more than I can well say. Author's address: Munich Center for Mathematical Philosophy, Ludwigstraße 31, Ludwig-Maximilians-Universit¨at,80539 M¨unchen, Germany; email: [email protected] 1 [W]e must bear in mind that the scientific or science-producing value of the efforts made to answer these old standing questions is not to be measured by the prospect they afford us of ultimately obtaining a solution, but by their effect in stimulating men to a thorough investigation of nature. To propose a scientific question presupposes scientific knowledge, and the questions which exercise men's minds in the present state of science may very likely be such that a little more knowledge would shew us that no answer is possible. The scientific value of the question, How do bodies act on one another at a distance? is to be found in the stimulus it has given to investigations into the properties of the intervening medium. James Clerk Maxwell \Attraction", Encyclopædia Brittanica (9th ed.) [B]etween a cogent and enlightened \realism" and a sophisticated \instrumentalism" there is no significant difference|no difference that makes a difference. Howard Stein \Yes, but. |Some Skeptical Remarks on Realism and Anti-Realism" Contents 1 Introduction 3 2 The Hole Argument6 3 Limits of Spacetimes 12 4 Pointless Constructions 21 5 The Debate between Substantivalists and Relationalists 26 6 An Embarassment of Spacetime Structures 28 6.1 Manifest Physicality . 29 6.2 Observability . 32 6.3 Physicality and Existence . 34 7 Valedictory Remarks on Realism and Instrumentalism, and the Structure of Our Knowledge of Physics 35 References 37 2 1 Introduction The revival of the debate in recent years in the broader community of philosophers over the ontic status of spacetime can trace its roots, in part, to its revival in the community of physicists. Be- lot (1996) and Belot and Earman (2001), for instance, claim that philosophers ought to take the debate seriously because many physicists do. I do not think that fact suffices as a good reason for philosophers to take the debate as interesting, much less even well posed, and so enter into it. The active work of physicists on our best physical theories should provide the fodder for the work of the philosopher of physics most of the time. Sometimes, however, the physicists are confused or just mistaken, and it is then our job to try to help set matters straight. I believe that is the case here.1 Other philosophers in recent work have taken inspiration from the traditional debates themselves. Maudlin (1993), for instance, after a pr`ecis of the debate in the 17th and 18th centuries and Kant's attempt to sidestep it, concludes, \[G]ranting that the world is an sich a spatiotemporal object, we must face a fundamental problem: Are space and time entities in their own right?" In this paper, I dispute that \must." A virtue of Maudlin's approach, which his work shares with that of many other contemporary philosophers no matter their inspiration, is the foundation of his arguments on the structures of our best physical theories and the use of those structures to guide metaphysical argument. I think the method falls short, however, in so far as it treats those structures in abstraction from their uses in actual scientific enterprises, both theoretical and experimental. This lacuna leaves the debate merely formulaic, without real content, at the mercy of clever sophistications without basis in real, empirically grounded scientific knowledge in the fullest sense. Stein (1994, p. 1) admirably sums up the situation as I see it. I quote him at length, as he says it better than I could: [L]et me . hazard a rough diagnosis of the reason why some things that are (in my view) true, important, and obvious tend to get lost sight of in our discussions. I think \lost sight of" is the right phrase: it is a matter of perspective, of directions of looking and lines of sight. As at an earlier time philosophy was affected by a disease of system-building|the ´espritde syst`eme against which a revulsion set in toward the end of the last century|so it has (I believe) in our own time been affected by an excess of what might be called the ´espritde technique. : a tendency both to concentrate on such matters of detail as allow of highly formal systematic treatment (which can lead to the neglect of important matters on which sensible even if vague things can be said), and (on the other hand), in treating matters of the latter sort, to subject them to quasi-technical elaboration beyond what, in the present state of knowledge, they can profitably bear. [W]hat I have described can be characterized rather precisely as a species of scholasticism. In so far as the word \scholasticism," in its application to medieval thought, has a pejorative connotation, it refers to a tendency to develop sterile technicalities|characterized by 1See Curiel (2001, 2009) for extensive arguments to this effect on closely related matters, and for a defence of this claim as a fruitful philosophical attitude. 3 ingenuity out of relation to fruitfulness; and to a tradition burdened by a large set of standard counterposed doctrines, with stores of arguments and counterarguments. In such a tradition, philosophical discussion becomes something like a series of games of chess, in which moves are largely drawn from a familiar repertoire, with occasional strokes of originality|whose effect is to increase the repertoire of known plays. In the spirit of Stein's diagnosis, rather than something formally sophisticated I'm going to propose something crude and simple: in order to try to avoid the sort of sterility that purely formal technical elaboration can lead to, we should look at the way that spacetime structures are used in practice to model real systems in order to try to make progress on issues closely related to those treated in the standard debate. For I do think that there are important, deep questions that we can make progress on in the vicinity of that debate, questions of the sort that Maxwell alludes to in the passage I quoted as one of this paper's epigraphs. As Maxwell intimates, however, in order for such questions to be investigated profitably, they must be such as to support and stimulate \the investigation of nature." And that, I submit, can be accomplished only when the questions bear on scientific knowledge in all its guises, as theoretical comprehension and understanding, as evidential warrant and interpretative tool in the attempt to assimilate novel experimental results, as technical and practical expertise in the design and performance of experiments, and as facility in the bringing together of theory and experiment in such a way that each may fruitfully inform the other. To that end, in this paper I will argue that the way to find the philosophically and scientifically fruitful gold in the metaphysical dross is to formulate and address the questions in a way that explicitly makes contact with both the theoretical and the experimental aspects of our best current knowledge about the kinds of physical system at issue.